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Piezoresistance effect of silicon
Abstract
The principle of the piezoresistance effect (PR) of n- and p-Si is explained by the carrier-transfer mechanism and the effective mass change. The origin of the shear piezoresistance coefficient π44 in n-Si is also a stress-induced effective mass change. A graphical representation of the PR on crystallographic orientations and the effect of impurity concentration on the PR are given for n- and p-Si. The non-linearity of the PR is also mentioned.
... Piezoresistive transduction has gained popularity among various sensing mechanisms due to its simple manufacturing processes, high sensitivity, and wide detection range [6,7]. This mechanism employs semiconductors and metals as sensing elements [8][9][10], with semiconductors exhibiting a significantly higher gauge factor (GF) than metals due to variations in the material's resistivity [11]. For instance, monocrystalline silicon can achieve a GF of 157 [12] while polycrystalline silicon (poly-Si or polysilicon) can reach up to 77 [13]. ...
... Figure 13a shows that the longitudinal GF has a mean value of 12.31 with a standard deviation, σs, of 0.33 while Figure 13b shows that the transversal GF has a mean value of −4.90 with σs = 0.35. These results indicate that piezoresistors oriented toward the applied strain are more sensitive to this external input, which aligns with the higher longitudinal piezoresistive coefficient of Si compared with the transversal coefficient [11]. Additionally, the non-linearity of the piezoresistors response was calculated and it was determined that the longitudinal GF has a non-linearity of 6.35%FS, 2.94%FS and 8.89%FS for piezoresistors with dimensions L/W of 5,10 and 20, respectively. ...
... The negative transversal GF is attributed to the fact that, for p-type Si, the transverse piezoresistive coefficient is negative (=−1.1). In contrast, the longitudinal piezoresistive coefficient is positive (=6.6) according to Y. Kanda [11]. This result sustains the assertion that the Al content in AlSiCu acts as a p+ dopant. ...
The development of low-temperature piezoresistive materials provides compatibility with standard silicon-based MEMS fabrication processes. Additionally, it enables the use of such material in flexible substrates, thereby expanding the potential for various device applications. This work demonstrates, for the first time, the fabrication of a 200 nm polycrystalline silicon thin film through a metal-induced crystallization process mediated by an AlSiCu alloy at temperatures as low as 450 °C on top of silicon and polyimide (PI) substrates. The resulting polycrystalline film structure exhibits crystallites with a size of approximately 58 nm, forming polysilicon (poly-Si) grains with diameters between 1–3 µm for Si substrates and 3–7 µm for flexible PI substrates. The mechanical and electrical properties of the poly-Si were experimentally conducted using microfabricated test structures containing piezoresistors formed by poly-Si with different dimensions. The poly-Si material reveals a longitudinal gauge factor (GF) of 12.31 and a transversal GF of −4.90, evaluated using a four-point bending setup. Additionally, the material has a linear temperature coefficient of resistance (TCR) of −2471 ppm/°C. These results illustrate the potential of using this low-temperature film for pressure, force, or temperature sensors. The developed film also demonstrated sensitivity to light, indicating that the developed material can also be explored in photo-sensitive applications.
... The piezoresistive effect of semiconductors, like silicon, is well known [Kand82,Kand91,Smit54]. It correlates a strain to a resistance change, which allows the measurement of strain within the semiconductor itself. ...
... The piezoresistive coefficient 11 depends on the temperature and the charge carrier density , which can be described by the dimensionless factor [Kand91]. ...
... Hence in addition to stress the resistance change Δ is influenced by the sheet resistance □ , the aspect ratio = / , the charge carrier density and the temperature . The latter dependence vanishes for sufficiently high charge carrier densities (≫ 10 20 cm -3 ) [Kand91]. From these parameters different design variations is derived in the next Section. ...
Stress in solar cells plays a crucial role in the reliability of photovoltaic (PV) modules.
The influences on stress are as diverse as the number of different materials in a PV
module and become more and more complex with the growing variety of PV modules
for different applications.
Within this dissertation, a set of 15 thermomechanical design rules is derived to support
and accelerate future PV module developments. Three methods are developed
and applied:
1. Thermomechanical finite element method simulations of PV module designs (FEM)
2. μ-Raman spectroscopy of laminated solar cells (μ-Raman)
3. Solar cell integrated stress sensors (SenSoCell®)
Furthermore, the concept of specific thermal expansion stiffness Ê_α = E · α · A_j · h is
introduced as a measure of how much thermal strain one material can induce in
another.
... To realize the appropriate scheme for the enhancement of sensitivity, it is important to note the basic properties of a piezoresistive cantilever-type nanomechanical sensor for surface stress sensing, i.e., piezocoefficient [38]. Because of its high piezocoefficient, p-type piezoresistors created by boron diffusion onto a single crystal silicon with (100) surface can be effectively utilized [125][126][127]. Assuming plain stress (i.e., = 0) owing to the intrinsically two-dimensional feature of surface stress, the relative resistance change can be described as follows [127,128]: ...
... Because of its high piezocoefficient, p-type piezoresistors created by boron diffusion onto a single crystal silicon with (100) surface can be effectively utilized [125][126][127]. Assuming plain stress (i.e., = 0) owing to the intrinsically two-dimensional feature of surface stress, the relative resistance change can be described as follows [127,128]: ...
Nanomechanical sensors have gained significant attention as powerful tools for detecting, distinguishing, and identifying target analytes, especially odors that are composed of a complex mixture of gaseous molecules. Nanomechanical sensors and their arrays are a promising platform for artificial olfaction in combination with data processing technologies, including machine learning techniques. This paper reviews the background of nanomechanical sensors, especially conventional cantilever-type sensors. Then, we focus on one of the optimized structures for static mode operation, a nanomechanical Membrane-type Surface stress Sensor (MSS), and discuss recent advances in MSS and their applications towards artificial olfaction.
... Among them, metal thin-film stress sensors usually use strain-volume-induced changes in metal or alloy resistance to measure stress, have the advantages of good stability, and are applicable to a wide range of temperatures, etc., but their sensitivity coefficient is low, and in order to obtain a larger output resistance, there needs to be a large number of winding metal resistors, resulting in a low degree of integration. Semiconductor thin-film stress sensors use strain-induced resistivity changes to measure stress [16][17][18], have high-sensitivity coefficients, and are easy to integrate and mass produce, but their preparation process is more complex, and signal processing is inconvenient. In addition, the traditional semiconductor thin-film stress sensors are mainly patch-type, using adhesive and other methods to combine with the measured parts, through stress transfer measurement [19][20][21][22][23]. ...
Current stress sensors for microsystems face integration challenges and complex signal decoding. This paper proposes a real-time uniaxially sensitive stress sensor. It is obtained by simple combinations of bar resistors using their sensitivity differences in different axes. With the aid of a Wheatstone bridge, the sensor can measure the uniaxial stress magnitude by simple calibration of the stress against the output voltage and detect the bidirectional stress magnitude and direction in a micro-zone by simple rotation. The theoretical sensitivity obtained from simulation is 0.087 mV/V·MPa when the X-bridge is stressed in the X-direction under 1 V of excitation, and the test sensitivity of the X-bridge prepared in this paper is 0.1 mV/V·MPa. The design is structurally and procedurally simple, exhibits better temperature stability, and reduces interface requirements, making it suitable for the health monitoring of multi-chip microsystem chips.
... Here, k-factors over 10 were achieved for Ni-DLC. The most typical semiconductor strain gauge material is silicon that can have k-factors up to 200 for p-type (110) single crystalline silicon [43], [44], [45]. For p-type poly crystalline silicon, values up to 25 [35] or even up to 34 [46], [47] were measured. ...
Many industrial production processes use sensors to generate information about the manufacturing process. In this way, monitoring machine tools ensures the proper functionality of the system and detects unexpected behavior due to, for example, material inhomogeneity, incorrect data input, temperature influence or tool wear. In large production machines, such as portal milling machines, the sensor equipment of guide carriages can be an important possibility since they are a standardized component and can be easily integrated into existing machines. Here, conventional polymer foil-based strain gauges show several disadvantages due to reproducibility and reliability of the sensor connection via adhesive. Thus, this article addresses the manufacturing of directly-deposited chromium thin-film strain gauges on a guide carriage with integrated programmable data pre-amplification. Tests with different sensor materials on steel substrates showed that chromium was the most suitable sensor material with a high k-factor. Then, one end face of the carriage was polished before sputtering an Al
2
O
3
insulation layer and a chromium sensor layer that was laser-structured afterward to produce two Wheatstone full-bridges at previously simulated sensor positions. In a tensile test stand, the calibration of the sensors took place in the two spatial directions perpendicular to the guide rail direction. With an additional sensor data fusion for the final interpretation of measured forces, it is shown that this sensor technology is suitable for force measurement at guide carriages.
... The Raman peak shifts from 516.51 to 514.66 cm − 1 under different strain levels above, results of which indicate the increasing applied strain within materials can lead to a left shift of the Raman peak of silicon. Thus, the piezoresistive effect of Si-NR is potentially attributed to alterations in lattice parameters caused by the applied strain, which subsequently affects the band structure of the Si-NR and can result in variations in carrier mobility (Kanda, 1991;Yang and Lu, 2013). For the device characteristics, Fig. 1g summarizes statistical results for GF of the IOP gauge and SE of the OST sensor, measured from 30 variable P&T@DG. ...
... Achieving high GF ratio at small voltage difference is difficult because it requires the electrical property depending significantly on bias voltage as well as strain. Table 1 lists GF ratio and switching voltage in various non-RTD sensors, such as ZnO and GaN/AlN nanowire tunneling transistors [5,51], Si flexoelectronic transistors [2,6], MoS 2 piezotronic device [66], two-dimensional SnS 2 Schottky diode [22], and graphene/MoS 2 field-effect transistor (FET) [97]. It suggests that our GF ratio is one or two orders of magnitude higher than that of reported strain sensors, and switching voltage is lower. ...
Developing emerging technologies in Internet of Things and artificial intelligence requires high-speed, low-power, high-sensitivity, and switchable-functionality strain sensors capable of sensing subtle mechanical stimuli in complex ambience. Resonant tunneling diodes (RTDs) are the good candidate for such sensing applications due to the ultrafast transport process, lower tunneling current, and negative differential resistance. However, notably enhancing sensing sensitivity remains one of the greatest challenges for RTD-related strain sensors. Here, we use piezotronic effect to improve sensing performance of strain sensors in double-barrier ZnO nanowire RTDs. This strain sensor not only possesses an ultrahigh gauge factor (GF) 390 GPa⁻¹, two orders of magnitude higher than these reported RTD-based strain sensors, but also can switch the sensitivity with a GF ratio of 160 by adjusting bias voltage in a small range of 0.2 V. By employing Landauer–Büttiker quantum transport theory, we uncover two primary factors governing piezotronic modulation of resonant tunneling transport, i.e., the strain-mediated polarization field for manipulation of quantized subband levels, and the interfacial polarization charges for adjustment of space charge region. These two mechanisms enable strain to induce the negative differential resistance, amplify the peak-valley current ratio, and diminish the resonant bias voltage. These performances can be engineered by the regulation of bias voltage, temperature, and device architectures. Moreover, a strain sensor capable of electrically switching sensing performance within sensitive and insensitive regimes is proposed. This study not only offers a deep insight into piezotronic modulation of resonant tunneling physics, but also advances the RTD towards highly sensitive and multifunctional sensor applications.
... Additionally, the inherent piezoresistive property of silicon makes it an attractive material for pressure sensors. Piezoresistivity in semiconductors like silicon and germanium has been extensively studied since the early 1950s [24] - [27]. Pressure-sensitive sensors can be made using either silicon resistors or transistors as the primary sensing element [28] - [33]. ...
Bioinspired robotics and smart prostheses have many applications in the healthcare sector. Patients can use them for rehabilitation or day-to-day assistance, allowing them to regain some agency over their movements. The most common way to make these smart artificial limbs is by adding a “human-like” electronic skin to detect force and emulate touch detection. This paper presents a fully integrated CMOS-based stress sensor design with a high dynamic range (100 kPa to 100 MPa) supported by an adaptive gain-controlled chopping amplifier. The sensor chip includes four identical sensing structures capable of measuring the chip’s local stress gradient and complete readout circuitry supporting data transfer via I2C protocol. The sensor takes 10.2 ms to measure through all four structures and goes into a low-power mode when not in use. The designed chip consumes a total current of ~300
μ
A for one complete operation cycle and ~30
μ
A during low power mode in simulations. Moreover, the complete design is CMOS-based, making it easier for large-scale commercial fabrication and more affordable for patients in the long run. This paper further proposes the concept of a tactile smart skin by integrating a network of sensor chips with flexible polymers.
... In p-or n-Si, piezoresistance is due to the carrier-transfer mechanism and the effective mass change [50]. Yamada et al investigated the nonlinearity in the piezoresistance of the ptype silicon [51]. ...
Monocrystalline bulk silicon with doped impurities has been the widely preferred piezoresistive material for the last few decades to realize micro-electromechanical system (MEMS) sensors. However, there has been a growing interest among researchers in the recent past to explore other piezoresistive materials with varied advantages in order to realize ultra-miniature high-sensitivity sensors for area-constrained applications. Of the various alternative piezoresistive materials, silicon nanowires (SiNWs) are an attractive choice due to their benefits of nanometre range dimensions, giant piezoresistive coefficients, and compatibility with the integrated circuit fabrication processes. This review article elucidates the fundamentals of piezoresistance and its existence in various materials, including silicon. It comprehends the piezoresistance effect in SiNWs based on two different biasing techniques, viz., (i) ungated and (ii) gated SiNWs. In addition, it presents the application of piezoresistive SiNWs in MEMS-based pressure sensors, acceleration sensors, flow sensors, resonators, and strain gauges.
... where, Δρ is the change in resistivity, ε is the strain and ν is called the Poisson's ratio which is used to relate the change in length to the change in width and thickness of the piezo-resistor. Single crystalline silicon (p-type 110) offers an intrinsic GF of up to 200 [14]. This makes silicon an ideal choice for microelectromechanical systems (MEMS) based pressure sensors requiring higher piezo-resistivity. ...
Annealing temperature is one of the key factors affecting the structural and electrical properties of aluminum induced crystalline silicon (AIC-Si) which also exhibits piezo-resistivity due to which it can be used to build pressure sensors. Herein, we deposited 115 nm of hydrogenated amorphous silicon (a-Si: H) over glass and Kapton at a low substrate temperature of 60 °C by hot-wire chemical vapor deposition (HWCVD). Over a-Si: H, 50 nm of aluminum (Al) layer was deposited at room temperature by physical vapor deposition (PVD). Four samples (Al/a-Si: H/substrate) with similar specifications were annealed at 350, 375, 400 and 425 °C respectively. Crystalline silicon (c-Si) was obtained on surface due to layer exchange during annealing. Through Raman spectroscopy, all the morphological structures on the surface were identified as c-Si and showed similar composition of Si (55–58 at%), Al (7–9 at%) and oxygen (33–36 at%) for all the samples. With the increase in annealing temperature, Raman peak corresponding to c-Si shifted from 518 to 519 cm⁻¹ and the average crystallite size was found to increase from 27 to 43 nm. During the crystallization process, Al got doped in Si and showed an increase in carrier concentration from 2.77 × 10¹⁸ cm⁻³ at 350 °C to 3.76 × 10¹⁹ cm⁻³ at 425 °C. Average crystallite size and carrier concentration had conflicting influence on carrier mobility as well as gauge factor (GF) and yielded a maximum GF of 12.3. The GF obtained was three to 6 times higher than that of materials conventionally used in strain gauges.
... Strain-sensitive characteristics in semiconductive materials and structures have been investigated extensively for developing various mechanical sensing devices, such as pressure sensors, accelerometers, and strain gauges [14,15]. Thanks to its high sensitivity, good linearity, simple fabrication, and electronic integration capability, piezoresistive effect is the most dominant mechanism for these applications [16,17]. ...
... Strain-sensitive characteristics in semiconductors have been studied extensively for developing a wide range of mechanical sensing devices, such as pressure sensors, strain gauges, and accelerometers [1,2]. It is widely accepted that the piezoresistive effect is one of the most dominant mechanisms for making these sensors thanks to its high sensitivity, great linearity, simple fabrication, electronic integration capability, and low power consumption [3][4][5]. ...
This paper investigates for the first time the piezojunction effect in heterojunctions under external bias for ul-trasensitive strain sensing. As a proof of concept, we used sensing devices made of 3C-SiC/Si heterostructure with vertically aligned electrodes. Applying the beam bending method to characterize the sensing effect, the bending strain was introduced along the typical orientation [100] or [110] on (100) Si plane. Experimental results show a linear relationship between the relative change in the forward current and the applied strain from 0 to 500 ppm, decreasing under the tensile strain while increasing under the compressive strain. At the forward bias of 8 V, the obtained gauge factors (GFs) are 199.7 for [100] orientation and 173.1 for [110] orientation, which significantly enhance about 630 % and 540 % compared to the highest GF of n-type 3C-SiC in the literature. Interestingly, the GFs of the n +-3C-SiC/p-Si heterostructure are positive in contrast to the negative GFs of n-3C-SiC thin films. The results were explained by the strain modulation on the band split and electron mass shift along the out-of-plane direction as well as by the change in the barrier height, depletion region width, and carrier concentrations under the forward bias. The ultrasensitive piezojunction effect in the 3C-SiC/Si heterojunction demonstrated in this study can pave the way toward developing ultrasensitive mechanical sensors.
... The sensitivity of conventional non-pure axial deformation accelerometers can be calculated using equation (1) [25,26]: ...
Microfabricated piezoresistive accelerometers with purely axially deformed piezoresistive beams have demonstrated high performance. However, the conventional design of such accelerometers requires complex theoretical calculations and specific dimensional conditions to achieve purely axial deformation, which inevitably increases the difficulty and cost of the design and manufacturing. We propose an innovative structure that can simply realize pure axial deformation of piezoresistive beams by eliminating the transverse displacement at both ends without tedious calculations. An accelerometer based on the structure was fabricated; both static and dynamic performances were tested. The results showed that the accelerometer had high sensitivity (2.44 mV g ⁻¹ with 5 V bias, without circuit amplification), low cross-axis sensitivity (1.56% and 0.49 %, respectively), and high natural frequency (11.4 kHz), with a measurement range of 0–100 g. This design method provides an easy approach for designing high-performance piezoresistive sensors.
... First, the piezoresistive effect means the change of electrical resistivity of a material when a mechanical strain/stress is applied. 32,33 For p-type Si, the valence band structures in the out-of-plane direction under different strain conditions are presented in Figure 1a 1 ,b 1 ,c 1 . Shifted downward by Λ = 0.0441 eV at k = 0, the spin−orbit split-off band (E SO ) is almost empty while holes are populated in the light hole band (E LH ) and the heavy hole band (E HH ). ...
This paper presents a novel self-powered mechanical sensing based on the vertical piezo-optoelectronic coupling in a 3C-SiC/Si heterojunction. The vertical piezo-optoelectronic coupling refers to the change of photogenerated voltage across the 3C-SiC/Si heterojunction upon application of mechanical stress or strain. The effect is elucidated under different photoexcitation conditions and under varying tensile and compressive strains. Experimental results show that the relationship between the vertical photovoltage and applied strain is highly linear, increasing under the tensile strain while decreasing under the compressive strain. The highest sensitivities to tensile and compressive strains are 0.146 and 0.058 μV/ppm/μW, respectively, which are about 220 and 360 times larger than those of the lateral piezo-optoelectronic coupling reported in literatures. These extremely large changes in vertical photovoltages are explained by the alteration in effective mass, energy band shift, and repopulation of photogenerated holes in out-of-plane, in-plane longitudinal, and in-plane transverse directions when strains are exerted on the heterojunction. The significant enhancement of strain sensitivity will pave the way for development of ultrasensitive and self-powered mechanical sensors based on the proposed vertical piezo-optoelectronic coupling.
... Temperature T acts via the temperature-dependent Hall mobility of the charge carriers [11], [41]. The cross-sensitivity to mechanical stress has its origin in piezoresistance and the piezo-Hall effect [11], [42]- [44]. In the former, pseudo-Hall signals are caused by shear components of the mechanical stress tensor. ...
For the first time, Bayesian sensor calibration is used to identify efficient calibration procedures for a sensor cross-sensitive to 2 parasitic influences. The object under study is a thermomechanically cross-sensitive sensor system for determining the magnetic induction
B . The packaged system comprises a Hall sensor, a stress sensor, and a temperature sensor. The three sensor signals are combined in a polynomial sensor response model with 11 parameters to determine B compensated for offset and cross-sensitivities. For the calibration, sensors are exposed to mechanical stress values between 0 and -68MPa, temperatures between -40 and 100 °C, and B values between -25 and 25mT. A sample of 35 sensors serves to extract the prior model parameter distribution of their fabrication run. Bayesian experimental design is applied to identify sets of 2 to 8 optimal calibration conditions under I-optimality and G-optimality. Bayesian inference then allows to obtain the posterior model parameter distribution of any uncalibrated sensor from the same run. Any such sensor is thereby turned into a B measuring device with individually quantified accuracy. The method was successfully applied to 15 validation sensors. In the case of I-optimality, the median root-mean-square (rms) σ values of the ±1σ confidence intervals for the extracted B values were found to be 113 to 71 μT after near-I-optimal calibrations based on 2 to 8 measurements, respectively. Over the entire range of temperature and mechanical stress and for applied |B |≤25mT, corresponding experimentally determined medians of the rms deviations between predicted and applied B values were found to be 89 to 71 μT. Analogous observations apply to G-optimality. In short, Bayesian calibration made it possible to obtain functional B sensors of known accuracy with significantly fewer calibration measurements than model parameters. This was enabled by prior knowledge collected by the thorough characterization of 35 prior-generating specimens.
... Research on piezoresistive characteristics of the elastic polymer-based sensor has shown that the sensitivity is dominated by the geometry of the structure and the stress/strain variation within the composite [54][55][56] . Due to the relatively small variations in the geometry of thin lm-like exible sensors, the change of strain energy density relative to the external contact force is considered as the main factor affecting the piezoresistive effect. ...
Tactile sensors are instrumental for developing the next generation of biologically inspired robotic prostheses with tactile feedback capability. However, current sensing technology is still less than ideal either in terms of sensitivity under high pressure or compliance with uneven working surfaces. Also, the fabrication of tactile sensors often requires the use of highly sophisticated and costly manufacturing processes further limiting the widespread application of the technology. Here, we challenge the current perspective and propose the use of an in-house 3D printing system to develop a new conformal tactile sensor with enhanced sensing performance. The ability of the sensor to detect multi-directional stimuli is achieved through the integration of the auxetic structure and interlocking features. The unique design of our sensor allows for an extended sensing range (from 0.1 to 0.26 MPa) whilst providing sensitivity on both normal and shear directions at 0.63 KPa − 1 and 0.92 N − 1 , respectively. This is further complemented by capacity of the sensor to detect small temperature variations between 40 and 90°C. To demonstrate the feasibility of our approach, the tactile sensor is printed in situ on the fingertip of an anthropomorphic robotic hand, the proximal femur head and lumbar vertebra. The results suggest that it is possible to gain sensorimotor control and temperature sensing ability in artificial upper limbs whilst monitoring the bone-on-bone load, thus opening the door to a new generation of tactile sensors with novel auxetic structure design and enhanced performance for application in human prosthetics.
... In the present work, four p-type piezoresistors are fabricated on the (100) oriented plane along the <110> direction. Therefore, ∆R/R 0 in Equation (1) can be expressed, according to [26], as ...
The optimal groove design of a MEMS piezoresistive pressure sensor for ultra-low pressure measurement is proposed in this work. Two designs of the local groove and one design of the annular groove are investigated. The sensitivity and linearity of the sensor are investigated due to the variations of two dimensionless geometric parameters of these grooves. The finite element method is used to determine the stress and deflection of the diaphragm in order to find the sensor performances. The sensor performances can be enhanced by creating the annular or local groove on the diaphragm with the optimal dimensionless groove depth and length. In contrast, the performances are diminished when the local groove is created on the beam at the piezoresistor. The sensitivity can be increased by increasing the dimensionless groove length and depth. However, to maintain low nonlinearity error, the annular and local grooves should be created on the top of the diaphragm. With the optimal designs of annular and local grooves, the net volume of the annular groove is four times greater than that of the local groove. Finally, the functional forms of the stress and deflection of the diaphragm are constructed for both annular and local groove cases.
... with the Fermi integral F s and its derivative F s as a function of the temperature and doping dependent Fermi energy E F , the Boltzmann constant k b , and temperature T [39], [41]- [43]. The doping concentration and temperature dependant Fermi energy for n-Si and p-Si is shown in Fig. 14a. ...
Emerging new communication standards like 5G or 6G aggravate the circuit design of radio-frequency generation systems as they constantly increase demand on high bandwidths, low latency, and high spectral purity. The utilization of high- Q oscillators, however, provides a possibility of optimisation of radio-frequency oscillators regarding their phase-noise performance in the overall system. This paper analyses one of the most promising electromechanical resonator devices, the resonant fin transistor with respect to its performance and application in oscillator circuit design. Several investigations regarding its working principle, design trade-offs and limits are carried out in this work. An oscillator circuit design is given for two variants of the resonant fin transistor device together with an outlook on its performance compared to other state-of-the-art radio-frequency oscillator designs. Following the performance analyses conducted throughout this work, the fundamental limit for the Q -factor of this resonator is investigated, challenging the validity of functionality of the resonant fin transistor and its potential for circuit applications.
... and can be used in either active Anderson et al., 2018) or passive (Rahafrooz and Pourkamali, 2011;Abbasalipour et al., 2018;Ramezany and Pourkamali, 2018;Zope et al., 2020) sensing schemes. These coefficients change depending on crystallographic orientation and have been studied extensively in silicon (Kanda, 1991). While it is prudent to use average or effective stress/strain values for hand calculations with these equations, these effects can also be modeled as position-dependent and solved via TCAD if a detailed mode shape is known from finite element analysis (Li et al., 2012). ...
Monolithic integration of Microelectromechanical Systems (MEMS) directly within CMOS technology offers enhanced functionality for integrated circuits (IC) and the potential improvement of system-level performance for MEMS devices in close proximity to biasing and sense circuits. While the bulk of CMOS-MEMS solutions involve post-processing of CMOS chips to define freely-suspended MEMS structures, there are key applications and conditions under which a solid, unreleased acoustic structure composed of the CMOS stack is preferred. Unreleased CMOS-MEMS devices benefit from lower barrier-to-entry with no post-processing of the CMOS chip, simplified packaging, robustness under acceleration and shock, stress gradient insensitivity, and opportunities for frequency scaling. This paper provides a review of advances in unreleased CMOS-MEMS devices over the past decade, with focus on dispersion engineering of guided waves in CMOS, acoustic confinement, CMOS-MEMS transducers, and large signal modeling. We discuss performance limits with standard capacitive transduction, with emphasis on performance boost with emerging CMOS materials including ferroelectrics under development for memory.
... [33,34] The sample mounted at the end of a cantilever beam produced magnetic torque = × in a magnetic field, and the resultant small deflection of the beam was detected electrically by measuring the change of the resistance of the cantilever beam. [29] The sensitivity of a cantilever is roughly given by the formula Δ = 4Δ = L 6 (2 ) 2 , [29] where ∆ is the resistance change, is the excitation voltage, ∆ is the output voltage from the bridge, L = 4.5 × 10 −10 m 2 ·N −1 is the longitudinal piezoresistive coefficient for Si in the [110] direction, [35] and = 4 µm is the leg width. The values correspond to the resistance fluctuation of ∆ / ∼ 4.4 × 10 −5 , and the enhanced resolution of the measurement was evaluated as ∼ 3.26 × 10 −12 N·m. ...
We report a study of fermiology, electrical anisotropy, and Fermi liquid properties in the layered ternary boride MoAlB, which could be peeled into two-dimensional (2D) metal borides (MBenes). By studying the quantum oscillations in comprehensive methods of magnetization, magnetothermoelectric power, and torque with the first-principle calculations, we reveal three types of bands in this system, including two 2D-like electronic bands and one complex three-dimensional-like hole band. Meanwhile, a large out-of-plane electrical anisotropy ( ρ bb / ρ aa ∼ 1100 and ρ bb / ρ cc ∼ 500, at 2 K) was observed, which is similar to those of the typical anisotropic semimetals but lower than those of some semiconductors (up to 10 ⁵ ). After calculating the Kadowaki–Woods ratio (KWR = A / γ ² ), we observed that the ratio of the in-plane A a , c / γ ² is closer to the universal trend, whereas the out-of-plane A b / γ ² severely deviates from the universality. This demonstrates a 2D Fermi liquid behavior. In addition, MoAlB cannot be unified using the modified KWR formula like other layered systems (Sr 2 RuO 4 and MoOCl 2 ). This unique feature necessitates further exploration of the Fermi liquid property of this layered molybdenum compound.
Background
Cardiovascular diseases (CVDs) are the leading cause of death globally, and almost one-half of all adults in the United States have at least one form of heart disease. This review focused on advanced technologies, genetic variables in CVD, and biomaterials used for organ-independent cardiovascular repair systems.
Objective
A variety of implantable and wearable devices, including biosensor-equipped cardiovascular stents and biocompatible cardiac patches, have been developed and evaluated. The incorporation of those strategies will hold a bright future in the management of CVD in advanced clinical practice.
Methods
This study employed widely used academic search systems, such as Google Scholar, PubMed, and Web of Science. Recent progress in diagnostic and treatment methods against CVD, as described in the content, are extensively examined. The innovative bioengineering, gene delivery, cell biology, and artificial intelligence–based technologies that will continuously revolutionize biomedical devices for cardiovascular repair and regeneration are also discussed. The novel, balanced, contemporary, query-based method adapted in this manuscript defined the extent to which an updated literature review could efficiently provide research on the evidence-based, comprehensive applicability of cardiovascular devices for clinical treatment against CVD.
Results
Advanced technologies along with artificial intelligence–based telehealth will be essential to create efficient implantable biomedical devices, including cardiovascular stents. The proper statistical approaches along with results from clinical studies including model-based risk probability prediction from genetic and physiological variables are integral for monitoring and treatment of CVD risk.
Conclusions
To overcome the current obstacles in cardiac repair and regeneration and achieve successful therapeutic applications, future interdisciplinary collaborative work is essential. Novel cardiovascular devices and their targeted treatments will accomplish enhanced health care delivery and improved therapeutic efficacy against CVD. As the review articles contain comprehensive sources for state-of-the-art evidence for clinicians, these high-quality reviews will serve as a first outline of the updated progress on cardiovascular devices before undertaking clinical studies.
Energy bandgap largely determines the optical and electronic properties of a semiconductor. Variable bandgap therefore makes versatile functionality possible in a single material. In layered material black phosphorus, the bandgap can be modulated by the number of layers; as a result, few-layer black phosphorus has discrete bandgap values that are relevant for opto-electronic applications in the spectral range from red, in monolayer, to mid-infrared in the bulk limit. Here, we further demonstrate continuous bandgap modulation by mechanical strain applied through flexible substrates. The strain-modulated bandgap significantly alters the charge transport in black phosphorus at room temperature; we for the first time observe a large piezo-resistive effect in black phosphorus field-effect transistors (FETs). The effect opens up opportunities for future development of electro-mechanical transducers based on black phosphorus, and we demonstrate strain gauges constructed from black phosphorus thin crystals.
In this work, we demonstrate an integrated, simple, yet highly sensitive parallel plate and co-planar capacitive pressure sensors on a silicone-based composite substrate that addresses the issue of low surface energy of silicone. The composite substrate exhibited flexibility and appropriate bonding strength after high-temperature vulcanization. Meanwhile, by utilizing de-ionized water in dielectric mixture (10% to 30%) micro pores in different sizes and distributions in the dielectric was realized as a novel solution to enhance its flexibility and thus its sensitivity. The parallel plate pressure capacitor exhibited adjustable detection sensitivity between 5.3 kPa
-1
to 6.6 kPa
-1
and the highest sensitivity outperformed existing demonstrations in literatures with large dynamic window between 0.05 kPa to 83.3 kPa with a resolution of 0.05 kPa and response time of 0.25 s. On the other hand, the co-planar proximity sensor showed supportiveness on real time detection, exhibiting a multifunctional sensing system together with the parallel plate pressure sensor. Related design, fabrication, evaluation, and discussion were thoroughly conducted in this work.
Strain sensors are essential to structural health monitoring technology. Currently, commercially available strain gauges exhibit limitations such as weak output signal, temperature sensitivity, nonlinearity, instability, and difficulties in mass production; however, the ever-expanding application scenarios of strain gauges have sparked a heightened demand for enhanced sensitivity and testing accuracy in strain detection. In this work, a novel, highly sensitive semiconductor strain sensor is developed and manufactured via the MEMS process. The sensor employs dopant silicon as its sensitive material, while its design ingeniously integrates silicon-sensitive grids to amplify the gauge factor (GF) and output signal. Through the implementation of a differential output structure, the temperature dependence of the semiconductor resistor can be mitigated. A platinum temperature resistor is, furthermore, integrated to compensate for the impact of temperature variations on the measurement caused by changes in silicon Young’s modulus. The sensor exhibits a nonlinear error of less than 0.5% within the range of 0– 196
, and it possesses a GF of 174, which is approximately 80 times greater than that of existing commercial strain gauges. The proposed sensor exhibits significant performance enhancements and holds promising potential for industrial applications in highly demanding structural health monitoring scenarios.
In this paper, an IoT-based biogas production volume monitoring system and digester pressure control have been developed. This system uses a fixed dome type digester with a semi-continuous filling method. A mixture of stale rice and water in a ratio of 1:2 was used as a substrate with a refill time of every 2 days. The pressure and volume of gas in the digester are measured using a pressure sensor and a flow sensor. In order to produce optimal gas volume, the pressure in the digester is controlled using the on-off method. The biogas pressure and volume data are displayed on the LCD screen and then sent to the IoT platform so that it can be monitored remotely via a smart phone. Pressure in the digester can be maintained between 0.326 psi to 0.652 psi. The system that has been designed can produce an average gas volume of 10.37 liters. Data transmission to the platform is carried out with an interval of 10 minutes with a delay in the travel time of sending data for one transmission of 8 seconds.
Integrating sensors within a complete readout system on a single die has become essential to the More-than-Moore philosophy. Mechanical stress, as one of the physical quantities of potential interest, provides various information from simple static to dynamic load. Integration of piezoresistive elements within a complete CMOS system has been achieved in many ways, and ground-laying effects have been studied and described in detail. To bring the mechanical and electrical domains closer together, a new concept is presented that allows an analytical and simulation-based approximation of the sensors’ behavior due to applied mechanical stress as part of established concepts in electronics. It is evaluated based on measured state-of-the-art sensor implementations and used to bring up an alternative architecture with enhanced and on-the-fly adaptive sensitivity. Simulations are used to then further evaluate any model errors due to second-order effects that have been neglected within the design process.
It has been demonstrated that piezoresistive beams in a purely axial deformation state significantly enhance the performance of piezoresistive accelerometer. Current solution to realize purely axial deformation of piezoresistive beams for high performance micro-accelerometer relies heavily on beam positions, which limits its design flexibility and the error tolerance in the fabrication process. In this paper, a novel structure with position independent pure axially deformed piezoresistive beams is proposed. By controlling synchronous displacements at both ends of piezoresistive beams, the pure axially stress states of the piezoresistive beams can be easily realized at any beam position without tedious theoretical calculations. The theoretical model was developed to understand the relationship between the displacement and the axial stress of the piezoresistive beams, as well as the natural frequency of the whole structure. Then, the correctness of the theoretical model was verified by finite element simulation and experiments. The results demonstrated that the accelerometer had an extremely high sensitivity of 2.44 mV/g/5 V (without circuit amplification), and a high natural frequency of 11.4 kHz.
An upgrade of the three innermost layers of the ALICE ITS, intended to be installed during the LHC Long Shutdown 3, is under development. The detector concept foresees the usage of curved, wafer-scale Monolithic Active Pixel Sensors. Extensive characterization studies of bent single ALPIDE chips (used for the current ITS), have been carried out to evaluate their performance under the mechanical stress involved in the bending process. These tests on small sensors have opened the way to the investigation of a large scale sensor: a full size demonstrator of a half-layer in a truly cylindrical shape based on so called super-ALPIDE chips. Such activity has required the development of special tools and procedures dedicated to bend and read out the new pixel matrix.
Micro-fabricated pressure sensors are presently one of the most used micro-electromechanical system devices in the industry. Notably, they have gained popularity in medical, automotive and aeronautical applications. In the present work, a sensor operating in the low-pressure range with piezoresistive sensing and having a bossed-diaphragm structure has been designed. The structure has been characterized through numerical simulations using a custom-made software featuring geometrically nonlinear 2D elements. This simulation tool enables fast iterative design along with capturing key features related to the drift in sensitivity with respect to doping concentration and temperature. The simulation results show that the designed sensor has a full scale output of 2.2 µV/V/Pa, a linear error of 0.05% over its operating range of 5 kPa and a thermal sensitivity shift of − 0.1%/oC.
The superiority of stress sensors over temperature sensors for detecting defects in solder joints was investigated. The effects of joint defects on device stress and temperature in a single-sided cooling structure were obtained via thermal stress simulation. The peripheral, edge, and central defects were assumed as the defect distributions. The central defects did not result in a remarkable occurrence rate of the stress waveform change. In contrast, the periphery and edge defects caused a large occurrence rate of the stress waveform change compared to that of the temperature. In general, the thermal strain of solder joints in a power module causes its initial degradation from the joint edge or periphery. Thus, the stress waveform provides useful information for detecting initial degradation. The change pattern of the temperature waveform because of the solder joint defects only caused an amplitude increase. In contrast, stress waveform changes exhibited four different patterns: amplitude increase, amplitude decrease, waveform inversion, and waveform disappearance. These results confirm that stress sensors are better than temperature sensors for detecting waveform changes caused by slight joint defects at peripheral or edge, particularly with a small number of sensors. Application of the data acquired via stress sensors to machine learning will allow estimation of the joint defect distribution. Furthermore, time-series stress waveform data can provide prognostics of solder joint degradation.
Multi-point scanning measurement, which is effective in eliminating motion errors of the stage in on-machine profile measurement, requires multiple displacement sensors of equal pitch to measure displacements simultaneously. However, it is not easy to arrange small sensors with high alignment accuracy when applying the multi-point method at a narrow pitch. In addition, if many sensors can be arranged in parallel, improvement in measurement accuracy can be expected. Therefore, a new micro electro mechanical system (MEMS) device for straightness measurement, one that integrates 10 cantilever displacement sensors, has been proposed. This device can be expected to solve the problem involved in the multi-point method because of the characteristics of MEMS, as the semiconductor processing method can make mechanical structures with high accuracy and it can easily make the device with many identical structures. The device is designed to measure waviness less than 100 μm in height. Ten cantilevers of 11 mm length are fabricated in parallel with 1.8 mm pitch on a side of a base substrate 20 mm square. The strain induced by a displacement of the probe placed near the front edge of the cantilever is detected as a change in the resistance of the piezo resistor at the foot of the cantilever. In the fabrication process of this device, crystal anisotropic etching is performed for 12 hours to form probes 250 μm high. A new fabrication process is also proposed in which a protective process is added to prevent damage to the circuits already formed during the etching. A prototype is investigated, and it is found that the resistance value increases about 0.45% in proportion to the displacement of 100 μm. It is therefore confirmed that this device has the basic ability to detect displacement.
The calibration of multisensor systems can cause significant costs in terms of time and resources, in particular when cross-sensitivities to parasitic influences are to be compensated. Successful calibration ensures the trustworthy subsequent operation of a sensor system, guaranteeing that one or several measurands of interest can be inferred from its output signals with specified uncertainty. As the present study shows, this goal can be reached by reduced calibration procedures with fewer calibration conditions than parameters needed to model the device response. This is achieved using Bayesian inference by combining calibration data of a sensor system with statistical prior information about the ensemble to which it belongs. Optimal reduced sets of calibration conditions are identified by the method of Bayesian experimental design. The method is demonstrated on a Hall-temperature sensor system whose nonlinear response model requires seven parameters in the temperature range between –30 °C and 150 °C and for magnetic field values B between –25mT and 25mT. For the prior, a multivariate normal distribution of the model parameters is acquired using 14 specimens of the sensor ensemble. I-optimal calibration at one, two, and three temperatures reduces the rms standard deviation of B inferred from sensor output signals from 203 μT before calibration down to 78 μT, 41 μT, and 34 μT, respectively. Similar conclusions apply to G-optimal calibration. The paper describes how to implement the Bayesian prior acquisition, inference, and experimental design. The proposed approach can help save resources and cut costs in sensor calibration.
Vanadium dioxide (VO2) is a phase transition material whose physical and electrical properties, such as resistance, significantly change at the critical temperature. Specifically, the piezoresistive property and, thus, the gauge factor may change considerably in VO2 thin films; however, studies focusing on this phenomenon remain limited. This study evaluated the gauge factor of VO2 thin films by varying the temperature and W doping concentration. VO2 films were deposited on a conventional Si wafer using the sol-gel method, followed by an annealing process. Samples were produced without W doping and with 0.3, 0.6, and 1.0 at% doping concentrations. Phase transitions were observed via resistance changes of one order of magnitude near-critical temperatures of ~60 °C for no doping, ~50 °C for 0.3 at%, and ~30 °C for 0.6 at%; the sample with a 1.0 at% concentration exhibited a linear resistance change, resulting in no phase transition. The X-ray diffraction pattern shifted with the temperature change and showed critical temperatures similar to those obtained from the resistance measurements. Additionally, the temperature dependence of the gauge factor was experimentally obtained based on the carrier concentration and mobility. The gauge factors obtained experimentally and those calculated from the carrier concentration and mobility were examined. A gauge factor of 350 was obtained, much larger than that of the conventionally used Si, near the critical temperature at each doping concentration. The feasibility of VO2 thin films as piezoresistive materials was thereby demonstrated.
MEMS device degradation due to aging and other factors is becoming a major concern because it will cause parametric deviations and catastrophic failures in the mechanical and structural subsystems. However, MEMS testing in general which needs specific sophisticated testing equipment is complicated and time-consuming. To solve these problems, this paper specifically introduces a built-in self-test method which based on the periodic observation of the temperature-dependent output signal. A packaging scheme is designed and the test circuit is built to conduct test experiments on MEMS pressure sensors with different ranges and materials. The experimental results show that this method can effectively test the performance and will not affect the continued normal operation of the sensor. Furthermore, some compensation is made to correct the output to greatly improve the accuracy and reliability. Low cost, ease of implementation, and possibility to monitor in real time are the main advantages.
Macroscopic defects such as corrosion in nonmagnetic Conductors Under Stress (CUS) are more universal than those within the zero-stress environment, and result in complicated characteristics regarding the electrical properties of the conductors. In this paper, Gradient-field Pulsed Eddy Current technique (GPEC) is intensively investigated for imaging and evaluation of corrosion in CUS. The influence of stress on electrical properties of nonmagnetic CUS with corrosion is analysed via multi-physics simulations and experiments. The correlations between characteristics of corrosion in CUS and the GPEC signal and its features are established and scrutinised. An image processing method reproducing defect images for quantitative assessment of detected corrosion in CUS is proposed.
The basic technique to measure force in any kind of wind tunnel balance is the measurement of the strain on an elastic spring that is deformed by the aerodynamic loads acting on the wind tunnel model. In this chapter the fundamentals of strain measurement with strain sensors are described. For wind tunnel balances two major types of strain sensors are used. The most widely used is the wire strain gauge sensor and the second most widely used is the semiconductor strain gauge. Although in principle optical strain gauges offer even higher resolution, to date balances constructed using such sensors have not operated with the same precision as conventional balances.
In this paper, we derive an analytical model to describe the response of longitudinal and transverse piezoresistors embedded in micro-cantilever biochemical sensors. This model estimates the relative change in resistance and sensitivity of the piezoresistive elements taking into consideration the biaxial stress profile induced by surface stress loadings, the dimensions of the piezoresistor, and its location within the cantilever. To demonstrate its applicability and usefulness, we utilize our model to construct an analytical model for a piezoresistor with a U-shaped configuration. The effect of variation in the piezoresistor and cantilever dimensions, as well as the piezoresistor location and Poisson’s ratio, on the relative change of resistance and sensitivity to the applied surface stress are examined. The analytical predictions show that low aspect ratio micro-cantilevered plates (i.e. wide cantilevers) are better suited for piezoresistors subject to surface stresses. Moreover, the analytical model results allow us to identify a set of preliminary piezoresistor dimensions to increase the sensitivity of p-type U-shaped piezoresistors embedded in rectangular micro-cantilevered plates. Limitations in the microfabrication techniques of piezoresistors are also discussed in the context of our model predictions. The model here presented can be readily extended to describe the response and sensitivity of other piezoresistor configurations such as a streamer.
This tutorial explores the many different ways that electrical resistance can be used to sense changes in the environment. Resistancebased sensors span a wide spectrum of transfer characteristics from the linear to the non-linear and from small, sub-Ohm changes to changes in resistance that span many orders of magnitude. Electronic interface circuits suitable for measuring these resistances range from those that convert sensor resistance to an analog voltage to those that generate a square wave whose frequency, duty cycle, or phase indicates resistance. In this tutorial, voltage dividers, Wheatstone bridges, current sources, and current pumps are discussed to represent the broad choices for converting resistance to an analog voltage. Oscillators, resistance-to-phase converters, direct interface circuits, and analog to digital converter circuits that convert signals directly from resistance to digital signals are also discussed. This tutorial seeks to provide the novice circuit or sensor designer with a place to start in selecting the right interface circuit for processing signals from resistance-based sensors. It also offers some additional interface circuit alternatives to the more experienced engineer.
Many recent investigations in the context of graphene nanoplatelets (GNPs) coatings report surface strain measurements by using piezoresistive sensing capabilities. An often underestimated problem is that the strain field is unknown and the principal strain components as well as their orientations must be determined. Herein, GNP films subjected to multiaxial strain are examined. Experimental results show that although the sensitivity to longitudinal strain is the highest, the ratio between transverse and longitudinal sensitivity exceeds 0.5. The sensitivity to shear strain is much lower. A model assisted study of a random network provides additional guidelines for the different electromechanical sensitivities. In practice, the GNP film is usually subjected to different strains simultaneously so that the multiaxial strain measurement becomes difficult. Therefore, two novel approaches for sensing plane strain components with circular GNP films are developed and successfully verified in experiments. The numerical approach is called strain‐differential electrical impedance tomography (SD‐EIT), where the proposed piezoresistive model elementwise in a finite element model is implemented and the strain components of a strain rosette are reconstructed. Moreover, an analytical approach is derived from SD‐EIT and exhibits further the opportunity to detect anomalies within the piezoresistive sensing behavior of GNP films. Graphene nanoplatelets (GNPs) films promote the formation of conductive paths with piezoresistive sensing capabilities. Herein, how the resistance of GNP film is affected by multiaxial strain is theoretically and experimentally examined. To accurately characterize the strain field with GNP films, novel methodologies are presented. The goal is to determine the principal strains in an unknown 2D strain field.
In the past years, piezo-conductive sensors have drawn great attention in both academic and industrial sectors. The piezo-conductive sensors made by inorganic semiconductors exhibited poor mechanical flexibility, restricting their further practical applications. In this study, we report the piezo-conductive sensors by a semiconducting polymer, poly(3,4-ethylenedioxythiophene) doped with tosylate ions (PEDOT:Tos) thin films. Systemically studies indicate that the piezo-conductive response of the PEDOT:Tos thin films is originated from the deformation of the PEDOT crystal cells and the stretched π–π distances induced by Tos. Moreover, the negative piezo-conductive effect, for the first time, is observed from PEDOT:Tos thin film under the pressure. A working mechanism is further proposed to interpret the transient from a positive to a negative piezo-conductive response within the PEDOT:Tos thin films. Our studies offer a facile route to approach effective piezo-conductive sensors based on conjugated polymers.
Introduction of structural modification and novel transduction materials to nanomechanical cantilever (NMC) sensor can bring considerable improvement in sensor performance leading to ultra-sensitive nanomechanical sensor platforms. This work reports development of an optimized and highly sensitive silicon MEMS Nanomechanical Membrane-Flexure (NMF) piezoresistive surface stress sensor. This MEMS structure consists of a circular adsorbate membrane suspended by four inverse trapezoidal flexures. The electromechanical transduction of the sensor is performed by integrating a high gauge factor low temperature sputter deposited Indium Tin Oxide (ITO) thin film as piezoresistor. The ITO thin film was experimentally characterized for extracting its electrical, mechanical, and electromechanical properties to assess its candidature in integrating as strain sensing element with nanomechanical sensors. The gauge factor of ITO thin film was measured using a high precision four-point bending fixture experimental setup. An ultra-thin ITO film deposited at room temperature with no oxygen flow and post annealing treatments exhibited a high negative gauge factor of -430, making it an excellent candidate in nanomechanical sensor platform. The incorporation of sputter deposited ITO thin film as piezoresistive layer obviated the need for doping in silicon which further reduced the fabrication process complexity for NMF sensor. The NMF sensor fabrication following SOI based silicon MEMS process along with device characterization have also been carried out as part of this work. The optimized design of piezoresistive NMF sensor exhibited an improved surface stress sensitivity of nearly 15 times higher than conventional cantilever sensor and thereby opening new possibilities in bio-chemical and environmental sensing applications. [2021-0127]
Nanomechanical sensors have been expected as a promising platform for many fields owing to their high versatility; almost any kind of materials can be applied as receptor layers. Among various types of nanomechanical sensors, recently developed Membrane-type Surface stress Sensor (MSS) has attracted much attention as a new platform for mobile and/or Internet of Things (IoT)-based applications because it realizes both high sensitivity and a compact system at the same time. This article introduces the development process of MSS and its working principle with basic/technical details.
Some packaging technologies of electronic devices introduce compressive biaxial stress and variable vertical stress. In unipolar MOS devices, stress variations typically only linearly affect drain current via carrier mobility. Collector currents of bipolar devices are additionally affected by variations in intrinsic carrier concentration. This leads to increased variability of key device parameters in the compressive stress regime. Reducing package induced compressive stress, or inducing tensile stress, should improve device variability due to local stress variations.
In this article, describe temperature influence on silicon bases diode. Besides, give results that is taken by simulation.
A transport theory which allows for anisotropy in the scattering processes is developed for semiconductors with multiple nondegenerate band edge points. It is found that the main effects of scattering on the distribution function over each ellipsoidal constant-energy surface can be described by a set of three relaxation times, one for each principal direction; these are the principal components of an energy-dependent relaxation-time tensor. This approximate solution can be used if all scattering processes either conserve energy or randomize velocities. Expressions for mobility, Hall effect, low- and high-field magnetoresistance, piezoresistance, and high-frequency dielectric constant are derived in terms of the relaxation-time tensor. For static-field transport properties the effect of anisotropic scattering is merely to weight each component of the effective-mass tensor, as it appears in the usual theory, with the reciprocal of the corresponding component of the relaxation-time tensor.The deformation-potential method of Bardeen and Shockley is generalized to include scattering by transverse as well as longitudinal acoustic modes. This generalized theory is used to calculate the acoustic contributions to the components of the relaxation-time tensor in terms of the effective masses, elastic constants, and a set of deformation-potential constants. For n silicon and n germanium, one of the two deformation-potential constants can be obtained from piezoresistance data. The other one can at present only be roughly estimated, e.g., from the anisotropy of magnetoresistance. Insertion of these constants into the theory yields a value for the acoustic mobility of n germanium which is in reasonable agreement with observation; a more accurate check of the theory may be possible when better input data are available. For n silicon, available data do not suffice for a check of the theory.
Uniaxial tension causes a change of resistivity in silicon and germanium of both n and p types. The complete tensor piezoresistance has been determined experimentally for these materials and expressed in terms of the pressure coefficient of resistivity and two simple shear coefficients. One of the shear coefficients for each of the materials is exceptionally large and cannot be explained in terms of previously known mechanisms. A possible microscopic mechanism proposed by C. Herring which could account for one large shear constant is discussed. This so called electron transfer effect arises in the structure of the energy bands of these semiconductors, and piezoresistance may therefore give important direct experimental information about this structure.
The nonlinear piezoresistance effect in p- and n-type silicon was measured. The first- and second-order coefficients in stress were obtained. The results for n-Si are in fairly good agreement with those deduced from the stress-dependent carrier transfer theory between the valleys. The nonlinearity of the longitudinal mode in p-Si and that of the transverse mode in n-Si both under the <110> stress suggest that a third-order effect cannot be ignored.
Nonlinear piezoresistance effects in p-type Si resistors of three surface impurity concentrations were measured at room temperature. Stresses up to 174 MPa were applied along the and directions by bending a silicon cantilever. We determined all of the second-order piezoresistance tensor components, assuming that resistivity is more sensitive to shear than dilation, and that the hydrostatic pressure coefficient is zero.
The nonlinear piezoresistance effect of n-type silicon was measured under and stresses at room temperature, from which the first- and second-order coefficients in stress were determined. Second-order piezoresistance expressions were deduced from a model based on the stress-dependent carrier transfer between the valleys. The experimental results are in fairly good agreement with the theoretical ones.
An energy band of a diamond lattice at X(k=(2pia)(1, 0, 0)) on the zone boundary is two-fold degenerate because of the presence of glide-reflection symmetries. The degeneracy of the conduction band Delta1 and Delta2' at X in silicon was lifted by applying a compressive uniaxial stress along the [011] direction, the effect of which has been observed by measuring a shift of the cyclotron resonance line for the [100] electrons. An expression for the line shift has been obtained in terms of a perturbation series. By evaluating the series using the orthogonal-plane-wave (OPW) results of Kleinman and Phillips, the Delta1-Delta2' band mixing ratio Xiu'DeltaE is determined to be Xiu'DeltaE=11.4+/-1.1. This result when combined with OPW estimate for DeltaE, the energy separation between Delta1 and Delta2' at the conduction band edge, yields the value Xiu'~5.7 eV for the deformation potential responsible for the band splitting at X. The lifting of the special degeneracy of the X1 states is interpreted from the viewpoint of the tetrahedral covalent bond responding to an applied mechanical force. The sign of the cyclotron-resonance line shift indicates that two nonbonding orbitals of a valence electron connecting two neighboring Si atoms are hybridized to make the energy of the bonding orbital lower than that of the antibonding orbital when the bond is compressed. Also from the experimental work, the following values of the electron effective masses have been determined: m⊥m=0.1905+/-0.0001, mIIm=0.9163+/-0.0004.
Cyclotron resonance of holes in unstressed or "cubic" silicon fails to specify uniquely the valence band parameters because of the complex shape of the warped energy surfaces. The application of uniaxial stresses to the crystal lifts the cubic symmetry and removes the degeneracy at k=0 of the valence band which is responsible for the warping of the surfaces. The ellipsoidal energy surfaces of the decoupled bands give cyclotron resonance masses amenable to simple interpretation. From the measured masses (at 1.26°K and ~9000 Mc/sec) the following quantities have been determined: the inverse mass band parameters (in units of ℏ22m0) A=-4.28+/-0.02, |B|=0.75+/-0.04, and |N|=9.36+/-0.10 the absolute value of the ratio of the band splitting deformation potentials |Du'Du|=1.31+/-0.03 and the signs of the quantities BDu
The valence band structure in silicon single crystals subjected to an external uniaxial stress is investigated. The cyclotron resonance line for holes in such crystals is predicted to display a significant shift with increasing stress, if the split band populated with holes is associated with the quantum number MJ=+/-12. This strain-induced shift is characterized by the following properties: (a) Its magnitude is of the order of 10% of the frequency for strains of the order of 2×10-3 (b) it is anisotropic with respect to the relative orientation of the external magnetic field to that of the stress; (c) it must be absent if the band populated with holes is associated with the quantum number MJ=+/-32. These properties in conjunction with the experimentally determined shifts, presented in the paper by Hensel and Feher, lead to a unique assignment of the band parameters which had been left ambiguous by previous experiments. A discussion of the line shape of hole resonance in a deformed crystal is also presented.
It is shown that the origin of the shear piezoresistance (PR) coefficient pi44 of n-type silicon is a stress-induced effective-mass change of individual valleys rather than the stress-induced intervalley electron transfer, which has long been believed to be the dominant source of PR in many-valley semiconductors. An orthorhombic stress destroys the rotational symmetry of the ellipsoidal valleys and induces large effective-mass changes due to the special character of the conduction-band edge of silicon. The effective-mass anisotropy then leads to a transverse voltage when the current is along [100]. This mechanism predicts a sign and a magnitude of pi44 for n-type Si that are consistent with experiments hitherto known.
The shear piezoresistance coefficients pi'66, pi'16 and pi'26 of p- and n- type silicon are plotted as a function of the crystal directions for orientations in the (100) plane. Silicon pressure and other mechanical sensors with a four-terminal gauge, such as a Hall effect-type device, utilizing the shear stress have been of much interest. The outputs of the sensors are proportional to the shear piezoresistance coefficient pi'66.
Origin of the longitudinal and transverse piezoresistance of p-type silicon diffused layers as measured and analyzed by Yamada, Nishihara, Shimada, Tanabe, Shimazoe and Matsuoka is explored theoretically. A model of stress decoupling of the degenerate valence band into two bands of prolate and oblate ellipsoidal energy surface is shown to explain the qualitative feature of anisotropy, temperature dependence and the order of magnitude of the linear coefficients. On this basis, a further comparison is proposed between the model and the nonlinearity for conductivity, so as to establish the origin.
The current change induced by uniaxial compression is calculated for the , , and orientations. The change in minority carrier mobility is considered to higher order for stress in addition to the change in minority carrier concentration. The differences of heavy hole mass and light hole mass and their stress dependence are taken. Experimentally obtained deformation potential constants are used. The minority carrier concentration decreases at low stress level and then increases rapidly with increasing stress. The orientation which shows the maximum current change corresponds to the direction of the rotating axis of conduction valley. The orientation dependence of the current change is in good agreement with that obtained experimentally for the uniaxial and anisotropic stress effects. In Ge, the apparent stress coefficient of band gap is obtained as -10.5× 10-12 eV cm2/dyn for the orientation.
Piezoresistivity measurements are carried out on heavily doped ion-implanted p-type resistors on the surfaces of cantilever beams cut from a (100) silicon wafer. Tensile and compressive stresses, up to 85 MPa along the left bracket 110 right bracket direction, are applied by bending the beams with a micrometer. Nonlinear effects are clearly seen in the measurements where the resistor contains sections both parallel and perpendicular to the stress. The results are analyzed in terms of the first- and second-order piezoresistance coefficients. Values of the piezoresistance coefficients are calculated using analytical expressions for the strain dependent energy-wave vector relations of the valence bands and the known deformation potentials. The results of the calculations are compared with the experimental data including some earlier measurements reported in literature. The piezoresistivity of doped layers on a silicon surface has been widely used for pressure sensor applications.
The elastic coefficients for an arbitrary rectangular coordinate system are calculated as a function of direction cosines in the crystal. Young's modulus,shear modulus, and Poisson's ratio are defined in general and values tabulated for some of the more important directions in the crystal. Graphs of these moduli are also plotted as a function of crystal direction for orientations in the (100) and (110) planes as well as planes determined by the [110] direction and any perpendicular direction.
Piezoresistive characteristics of a diffused layer on the surface of a semiconductor having a cubic crystallographic structure are analyzed. The surface is assumed free of external forces, and the current component normal to the surface within the layer is assumed zero. The equations derived are useful in the design of diffused piezoresistive electromechanical transducers. The electric fields in the layer are related to the sheet current densities and the stresses by diffused piezoresistive coefficients, which are defined in integral form. These coefficients are functions of the fundamental piezoresistive coefficients, the crystal orientation, and the unstressed conductivity profile function in the layer, but are independent of the layer thickness. The coefficient of major interest is numerically evaluated as a function of surface impurity concentration for p‐type silicon and n‐type germanium‐diffused layers with Gaussian and complementary error function impurity distributions. Measurements on diffused samples are in agreement with the analysis. The magnitude of a nonlinearity in layer piezoresistance arising from the variations of the bulk coefficients with doping is estimated.
The piezoresistive properties of n‐ and p‐type layers formed by the diffusion of impurities into silicon have been investigated. The values of the three piezoresistance coefficients and the temperature dependence of the large coefficients have been measured on layers having surface concentration values from 1018 to 1021 cm-3. The piezoresistance effect in p‐type diffused layers follows qualitatively the behavior expected in a degenerate semiconductor. n‐type layers having high surface concentration values show a change in the symmetry of the piezoresistance effect at room temperature and a decrease in the coefficient π 11 at lower temperatures. A discussion of the piezoresistance effect in diffused layers and its relation to the piezoresistance effect in uniformly doped material is also given.
Principles of a varied group of new semiconducting, piezoresistive stress and strain transducers are outlined. These devices have in common the utilization of the transverse or shear piezoresistive effect. One group of devices consists of gauges in the form of a thin rectangular sheet which is bonded to the test piece, and whose resistance change can be expressed as a simple function of the principal stresses in the gauge. Two special gauges in this group are described. In one, the resistance change is proportional to the sum of the principal biaxial stresses for any orientation of the gauge on the test piece. In the other, the resistance change is proportional only to longitudinal stress components, being independent of transverse stress components. Also described are: a four‐terminal gauge for complete determination of biaxial stresses, full‐bridge gauges made from a single crystal, load cells of low compliance, new torque transducers, and diffusion techniques for making some of the foregoing. The devices are illustrated in terms of germanium and silicon but extension to other semiconductors is straightforward.
The longitudinal and transverse piezoresistance coefficients, Π(300 K), at room temperature are plotted as a function of the crystal directions for orientations in the
The nonlinearity of the piezoresistance effect of p-type layers diffused into the {110} silicon plane has been investigated. An expression which contains higher order stress terms and can treat the piezoresistance effect quantitatively has been derived. It has been found that third-order stress terms are sufficient to give a good approximation of the effect. The expression coefficients have been determined experimentally using a silicon cantilever on which p-type diffused layers having surface concentration values from 1018to 1019cm-3are formed. Nonlinearity in the case where the longitudinal axis of the cantilever is perpendicular to the direction of current flow is greater than that in the case where it is parallel to the direction of current flow under both tensile and compressive stresses. Using the new expression, it has been confirmed that results of numerical analysis on the nonlinearity of trial silicon piezoresistive pressure sensors agree well with experimental results.
Second-order piezoresistance of p-Si
- Matsuda